(covers information from several alternate timelines)
The Krenim Imperium was the sovereign state of the Krenim people, located in Grid 005 of the Delta Quadrant, 65,000 light-years from Earth. The Krenim rose to power based on their mastery of temporal science, which allowed them to create fearsome weapons such as chroniton torpedoes that could penetrate deflector shields. At its height, the Imperium spanned 5,000 parsecs and controlled thousands of warp-capable vessels, over 200 star systems, and some 900 planets.
In the 2170s, the Imperium had declined greatly due to conflict with the Rilnar. Annorax, a Krenim military commander and temporal scientist, sought to reverse this state of affairs by building a weapon ship that could erase targets from the space-time continuum. With it, Annorax destroyed the Rilnar and restored his people to glory. However, the elimination of the Rilnar indirectly led to a plague that devastated the Krenim, necessitating another temporal incursion. Over the next two centuries, Annorax erased countless civilizations from history, but could never achieve the full restoration of the Imperium that he desired. (VOY: "Year of Hell", "Year of Hell, Part II")
In one possible timeline, the USS Voyager encountered the Krenim on stardate 50973. Over the following year (dubbed the "Year of Hell" by the Voyager crew), Voyager suffered severe damage and heavy casualties battling Krenim warships as it traversed the Imperium. (VOY: "Before and After")
In another possible timeline, the USS Voyager encountered the Krenim in mid-2374. The region was then dominated by the Zahl, whose elimination by Annorax resulted in a 98% restoration. Again, the Voyager crew endured a "Year of Hell", battling the warships of the restored Imperium. However, in this timeline they managed to develop temporal shielding to defend against chroniton torpedoes. Unexpectedly, the shielding also interfered with Annorax's temporal calculations, leading him to inadvertently reduce the Imperium to a pre-warp state with the erasure of the Garenor. Annorax attempted to erase Voyager to correct this mistake, but failed to do so.
Ultimately, the Voyager crew forged an alliance with the Mawasi and the Nihydron and attacked the weapon ship. Captain Kathryn Janeway set Voyager to collide with the weapon ship, triggering a temporal incursion that erased the ship from history. The original timeline, in which the Imperium was a medium power in contest with its neighbors, was restored. In this timeline, Voyager peacefully circumvented Krenim space on the advice of a Krenim commander. (VOY: "Year of Hell", "Year of Hell, Part II")
Trailers for Star Trek Online's Delta Rising expansion showed a vessel similar to the Krenim temporal weapon ship. However, an early mission features a throwaway mention that the Imperium had been defeated by an as-yet-unknown force, which later turns out to be the Vaadwaur.
A mission released later revealed that a lone Krenim planet survived the destruction of the Imperium by adapting Annorax's temporal technologies to shift the planet out of the timeline. The surviving Krenim ally with the Federation/Klingon/Romulan alliance in exchange for aid against the Vaadwaur.
In the novel A Pocket Full of Lies, following the events of the Year of Hell, the Krenim of the new timeline have established a variation of the Department of Temporal Investigations known as the Krenim Temporal Defense Agency. In contrast to the DTI, the Agency's goal appeared to be to use time travel to subtly ensure Krenim supremacy in the present timeline, rather than simply preserve the current history, to the extent that they altered a timeline where their past enemies, the Rilnar and the Zahl, lived on a peaceful near-utopian planet, in favor of a timeline where the two were engaged in a protracted and pointless conflict on the same planet, because the peaceful timeline restricted Krenim expansion. Having discovered 'log buoys' created by Voyager during the original timeline that were protected from changes to history by Borg phase technology, the Krenim attempted to eliminate Voyager to prevent the crew affecting their history, but when this attack simply briefly fractured Voyager across multiple time periods in "Shattered", they abducted a version of Janeway from the ship and manipulated her into becoming a leader of the Rilnar against the Zahl during a planetary conflict. Having learned about the Krenim manipulation, Voyager managed to rescue the alternate Janeway, who was taken into an alternate past to raise her daughter – conceived with a Krenim who posed as a Rilnar to manipulate her – as part of an attempt by Q to make up for some of the hardships Janeway had endured.